We study a general class of partially linear transformation models, which extend linear transformation models by incorporating nonlinear covariate effects in survival data analysis. A new martingale-based estimating equation approach, consisting of both global and kernel-weighted local estimation equations, is developed for estimating the parametric and nonparametric covariate effects in a unif...

In this paper we introduce a new type of nets with distributed resources : resource transformation nets (RT-nets). A new calculus based on Horn fragment of Multi-pllcatlve Linear Logic is proposed for this class of models. Theorem of completness is proved.

Functional linear regression has been widely used to model the relationship between a scalar response and functional predictors. If the original data do not satisfy the linear assumption, an intuitive solution is to perform some transformation such that transformed data will be linearly related. The problem of finding such transformations has been rather neglected in the development of function...

Empirical likelihood inferential procedure is proposed for right censored survival data under linear transformation models, which include the commonly used proportional hazards model as a special case. A log-empirical likelihood ratio test statistic for the regression coefficients is developed. We show that the proposed logempirical likelihood ratio test statistic converges to a standard chi-sq...

In this paper, a new voting system model is introduced as a linear transformation model. The size of compartmental populations in each political group corresponding to every voted subject, the population weights, the weighted votes policy against each political group, the “Yes” and “No” rates, the “No” rejection policy and the “Yes” increase policy are the inputs / outputs of the introduced lin...

(1) For a function f : A→ B, we call A the domain, B the co-domain, f(A) the range, and f−1(b), for any b ∈ B, the fiber (or inverse image or pre-image) of b. For a subset S of B, f−1(B) = ⋃ b∈S f −1(b). (2) The sizes of fibers can be used to characterize injectivity (each fiber has size at most one), surjectivity (each fiber is non-empty), and bijectivity (each fiber has size exactly one). (3)...

Let L be a quasi-definite linear functional defined on the linear space of polynomials with real coefficients. In the literature, three canonical transformations of this functional are studied: xL, L + Cδ(x) and x L + Cδ(x) where δ(x) denotes the linear functional (δ(x))(xk) = δk,0, and δk,0 is the Kronecker symbol. Let us consider the sequence of monic polynomials orthogonal with respect to L....

We consider the following signal recovery problem: given a measurement matrix Φ ∈ Rn×p and a noisy observation vector c ∈ R constructed from c = Φθ∗ + where ∈ R is the noise vector whose entries follow i.i.d. centered sub-Gaussian distribution, how to recover the signal θ∗ if Dθ∗ is sparse under a linear transformation D ∈ Rm×p? One natural method using convex optimization is to solve the follo...

Generally, digital watermark can be embedded in any copyright image whose size is not larger than it. The watermarking schemes can be classified into two categories: spatial domain approach or transform domain approach. Previous works have shown that the transform domain scheme is typically more robust to noise, common image processing, and compression when compared with the spatial transform s...